IMHO - Wear your uniform, proudly, when you travel. It's totally OK - people appreciate it and it signals who you are.
Yes, wear a leave or liberty uniform. Army and Air Force can and do travel in BDU/ACU - very common and for them it's well inside the norm. For the Sea Services, the Summer Kahki (not wash Kahkis), Summer White or SDB is totally appropriate. Marines know what to do - I always thought the Kahki shirt and blue trousers were the way to go - very sharp for the warmer months.
Make sure you wear all your ribbons and wings and such, and don't be afraid to tell people what they all mean when people ask (they will).
People will be generous with service members in uniform, in public. Don't expect it, but don't be surprised either - simply be gracious and say thank you!
Edit - the local news here covered a family welcoming a young marine home from Iraq - on leave. He was on tv, filed getting off the Delta flight here at CVG in his desert utility uniform (the digital desert cammies). He was clearly USMC - so I guess there is an excpetion for Marines traveling from a combat zone.